BGE Animated rig freezes when rig goes off-screen... Can I make it not?
Any animation that is not seen by the active camera is culled, this is called frustum-culling. As for a solution for it, I am not 100% sure this is a solution, but you can disable frustum culling for a particular camera at run-time with the following code. KX_Camera.frustum_culling
Which is layman terms looks something like this.
import bge

def main(self):

  self.owner.scene.cameras[&quot;Camera_Name&quot;].frustum_culling = False

There is also another option called KX_Scene.activity_culling. Again, I am not sure exactly if this only applies to object logic, and not also object animation. The code for it can be found below.
import bge

def main(self):

  self.owner.scene.activity_culling = False